Using synthetic division (Ruffini's Rule), perform the following division:

__Determine our root divisor:__ To find our root, we solve the divisor equation x - 7 = 0

We add 7 to each side of the equation to get x - 7 + 7 = 0 + 7

Therefore, our root becomes x = 7

__Step 1: Write down our coefficients horizontally and our root of 7 to the left:__ __Step 2: Bring down the first coefficient of __**6** __Step 3: Multiply our root of __**7** by our last result of **6** to get **42** and put that in column 2: __Step 4: Add the new entry of __**42** to our coefficient of **1** to get **43** and put this in the answer column 2: __Step 5: Multiply our root of __**7** by our last result of **43** to get **301** and put that in column 3: __Step 6: Add the new entry of __**301** to our coefficient of **0** to get **301** and put this in the answer column 3: | 6 | 1 | ** 0** | -3 |

7 | | 42 | ** 301** | |

| 6 | 43 | ** 301** | |

__Step 7: Multiply our root of __**7** by our last result of **301** to get **2107** and put that in column 4: | 6 | 1 | 0 | -3 |

**7** | | 42 | 301 | ** 2107** |

| 6 | 43 | ** 301** | |

__Step 8: Add the new entry of __**2107** to our coefficient of **-3** to get **2104** and put this in the answer column 4: | 6 | 1 | 0 | ** -3** |

7 | | 42 | 301 | ** 2107** |

| 6 | 43 | 301 | ** 2104** |

Our synthetic division is complete. The values in our results row form a new equation, which has a degree 1 less than our original equation shown below:

Leading Answer Term = x

^{(3 - 1)} = x

^{2} Since the last number in our result line of 2104 does not equal 0, our answer will have a remainder. We take this term and divide it by our (x - r) root which is x - 7 shown below in our answer: